A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g. comprising part of, one, or several dies) on a substrate (e.g. a silicon wafer). Transfer of the pattern is typically via imaging onto a layer of radiation-sensitive material (resist) provided on the substrate. In general, a single substrate will contain a network of adjacent target portions that are successively patterned. Known lithographic apparatus include so-called steppers, in which each target portion is irradiated by exposing an entire pattern onto the target portion at one time, and so-called scanners, in which each target portion is irradiated by scanning the pattern through a radiation beam in a given direction (the scanning”-direction) while synchronously scanning the substrate parallel or anti parallel to this direction. It is also possible to transfer the pattern from the patterning device to the substrate by imprinting the pattern onto the substrate.
In order to monitor the lithographic process, one or more parameters of the patterned substrate, for example the overlay error between successive layers formed in or on it, are typically measured. There are various techniques for making measurements of the microscopic structures formed in a lithographic process, including the use of a scanning electron microscope and various specialized tools. One form of specialized inspection tool is a scatterometer in which a beam of radiation is directed onto a target on the surface of the substrate and one or more properties of the scattered or reflected beam are measured. By comparing one or more properties of the beam before and after it has been reflected or scattered by the substrate, one or more properties of the substrate may be determined. This may be done, for example, by comparing the reflected beam with data stored in a library of known measurements associated with a known substrate property. Two main types of scatterometer are known. A spectroscopic scatterometer directs a broadband radiation beam onto the substrate and measures the spectrum (intensity as a function of wavelength) of the radiation scattered into a particular narrow angular range. An angularly resolved scatterometer uses a monochromatic radiation beam and measures the intensity of the scattered radiation as a function of angle. An ellipsometer also measures polarization state.
There are two basic methods to determine the value of a parameter of interest of the target, e.g. critical dimension (CD), from the data (referred to as a spectrum) obtained from the scatterometer: iterative modeling and library searching. In the iterative modeling technique, a theoretical model of the target structure is used to calculate the spectrum that would be obtained from the target as a function of the parameter of interest. Starting with an initial or seed value, a predicted spectrum is calculated and compared to the measured spectrum so that the estimation of the parameter value can be improved. This process is repeated for a number of iterations until the predicted spectrum matches the measured spectrum to within a desired margin of error at which point it is assumed that the actual value of the parameter is equal to the predicted value of the parameter used to obtain the predicted spectrum to within a desired degree of precision.
In a library search, a library of predicted spectra is constructed, again using a model relating spectra to parameter values, and the measured spectra is compared to the library entries to determine the closest match. Interpolation between entries can be used to increase accuracy. The number of entries in the library is determined by the range of possible parameter values expected, which is dependent on how accurately the parameter value can be guessed in advance, and the desired accuracy of measurement.
In almost all cases, several parameters of the target may vary and affect the measured spectrum. The time taken to construct and search a library and to perform an iteration tends to increase exponentially with an increase in the number of parameters. Further, the number of iterations required to achieve a desired level of accuracy may increase dramatically with error in the initial guess.
Furthermore, the accuracy is limited by the combination of the signal to noise ratio of the scatterometer and the condition number of the Jacobian matrix, the latter representing the derivative of the scatterometry signal with respect to each of the measurement parameters. This condition number gets worse, and hence the accuracy gets worse, with increasing number of measurement parameters. As an example, the accuracy of CD measurement may improve by a factor of between 3 and 100 when changing from a 3-parameter model of the target structure to a 1-parameter model by setting the other parameters to a fixed value.